Hi Jenny,
Having gone through the process of designing and building an 8 x 20 camera a couple of years ago, I can safely say that it can be a complicated and long process to go through depending on how exact you want things to be and how dedicated you are to the final look of the product. I used Makori (very similar to Mahogany) and it worked very well.
Assuming you have the tools (table saw, good router, access to a planer/jointer) and the experience in wood working, it can be a very enjoyable experience. If you don't have the tools, you can do what Jim Fitzgerald did with the two cameras he built and do it all by hand in his apartment (but he's slightly crazy as some of us know). Contact him if you want his advice - he will be glad to talk about it.
You can do everything basically from scratch including making your own bellows which is what I did. or you can do like some have suggested and get an old beat up camera cheap and salvage the parts. After going throught the experience, I would recommend that latter and use what you can fine from other cameras. It will make the process much easier and getting the metal parts and pieces will contribute to probably a tighter fitting and operating camera. If I had to do it all over again, that is the way I would go.
Regarding the camera type, there are basically three different types to consider - a monorail type (like a Bender), a drop bed (like an old Kodak or Korona), and a double or triple extension bed (like a deardorf or newer modern types). The monorail will be less flexible in the field but will likely be the easiest to build. The drop bed will be the easier to build from scratch than the Deardorf style but may have stability problems with long lenses. The Deardorf style will likely be the most stable to use but more complicated to build. Just my 2 cents worth.
Regarding building your own 4 x 5 camera (as opposed to building one 8 x 10 or larger) - buying a used 4 x camera from Ebay is not expensive and you may actually be spending more to make one yourself. If you want to build it for the whole experience and have your own hand made camera to use, that's a different thing altogether. There is something about using your own camera that you spent all that time working on it yourself.
Hope this helps. Good luck in your experience.